Simplify; express your answer in exponential form. Assume $q\neq 0, r\neq 0$. $\dfrac{{(q^{4})^{3}}}{{(q^{5}r^{4})^{5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{4}}$ to the exponent ${3}$ . Now ${4 \times 3 = 12}$ , so ${(q^{4})^{3} = q^{12}}$ In the denominator, we can use the distributive property of exponents. ${(q^{5}r^{4})^{5} = (q^{5})^{5}(r^{4})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{4})^{3}}}{{(q^{5}r^{4})^{5}}} = \dfrac{{q^{12}}}{{q^{25}r^{20}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{12}}}{{q^{25}r^{20}}} = \dfrac{{q^{12}}}{{q^{25}}} \cdot \dfrac{{1}}{{r^{20}}} = q^{{12} - {25}} \cdot r^{- {20}} = q^{-13}r^{-20}$.